Which of the following numbers is a multiple of 13? ${52,61,82,83,116}$
The multiples of $13$ are $13$ $26$ $39$ $52$ ..... In general, any number that leaves no remainder when divided by $13$ is considered a multiple of $13$ We can start by dividing each of our answer choices by $13$ $52 \div 13 = 4$ $61 \div 13 = 4\text{ R }9$ $82 \div 13 = 6\text{ R }4$ $83 \div 13 = 6\text{ R }5$ $116 \div 13 = 8\text{ R }12$ The only answer choice that leaves no remainder after the division is $52$ $ 4$ $13$ $52$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $52$ $52 = 2\times2\times13 13 = 13$ Therefore the only multiple of $13$ out of our choices is $52$. We can say that $52$ is divisible by $13$.